Realizations of the monster Lie algebra

DOI10.1007/BF01614075zbMath0828.17029arXivhep-th/9408037WikidataQ56429235 ScholiaQ56429235MaRDI QIDQ1805385

James Lepowsky, Elizabeth Jurisich, Robert Lee Wilson

Publication date: 19 December 1995

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9408037

zbMATH Keywords

free Lie algebramoonshine moduleKac-Moody Lie algebrastandard modulesCartan subalgebrassimple rootsexplicit constructionmonster Lie algebramonster simple group

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Simple groups: sporadic groups (20D08) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Identities, free Lie (super)algebras (17B01)

Related Items

Generalized Kac-Moody algebras and some related topics, Beyond Borcherds Lie algebras and inside, A resolution for standard modules of Borcherds Lie algebras, Dimension formula for graded Lie algebras and its applications, Moonshine, Constructing a Lie group analog for the Monster Lie algebra, Fricke Lie algebras and the genus zero property in Moonshine, Generalized moonshine. II: Borcherds products, Vertex operators for imaginary \(\mathfrak{gl}_2\) subalgebras of the Monster Lie algebra, Borcherds–Bozec algebras, root multiplicities and the Schofield construction, Conformal field theory and elliptic cohomology, Graded Lie superalgebras and the superdimension formula

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\lambda\)-rings and the representation theory of the symmetric group
• Generalized Kac-Moody algebras
• Central extensions of generalized Kac-Moody algebras
• Lie algebra homology and the Macdonald-Kac formulas
• Generalized Kac-Moody algebras and the modular function \(j\)
• The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. I: The existence of the resolution
• On the fundamental representation of Borcherds algebras with one imaginary simple root
• Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra
• Monstrous moonshine and monstrous Lie superalgebras
• Replication formulae for \(n| h\)-type Hauptmoduls
• A new class of Lie algebras
• Generalized Verma modules, loop space cohomology and MacDonald-type identities
• A natural representation of the Fischer-Griess Monster with the modular function J as character
• Monstrous Moonshine
• On defining relations of certain infinite-dimensional Lie algebras
• Rational Hauptmoduls are Replicable
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH